In a 13x9-inch glass baking dish, combine all marinade ingredients and mix well to combine. Add cubed meat, tossing to coat it well. Cover and refrigerate for 24 hours, periodically turning the meat to coat it with marinade.
Heat grill and lightly rub cooking grid with vegetable oil to keep meat from sticking. Evenly divide meat cubes and thread them on six metal skewers. Discard marinade. Grill meat over medium heat until cooked and nicely browned on all sides, about 10 to 15 minutes.
Meanwhile, lightly butter rolls or brush them lightly with olive oil and place them under the broiler, or face-down on the grill, just until lightly browned. Remove meat from skewers, and place it directly into heated rolls.
Yield: 6 sandwiches.
Note: If desired, make additional marinade to drizzle over the spiedies; do not re-use meat marinade. Spiedies can be a bit dry without the additional sauce.